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In this letter, efficient performance bounds for multihop wireless communications systems with non-regenerative blind relays over non-identical Nakagami-n (Rice), Nakagami-m and Nakagami-q (Hoyt) generalized fading channels, are presented. More specifically, the end-to-end signal-to-noise ratio (SNR) is formulated and upper bounded by using the well-known inequality between harmonic and geometric mean of positive random variables. This bound is used to study important system's performance metrics: i) the moments of the end-to-end SNR which are obtained in closed-forms, and ii) the outage probability and the average error probability for coherent and non-coherent modulations, which are accurately approximated using the moments-based approach. Furthermore, new analytical formulae are derived for the gain of previously proposed semi-blind relays in generalized fading environments. These kind of relays are used in numerical examples and computer simulations to verify the accuracy and to show the tightness of the proposed bounds.